Neural Network Material Modelling

Ghaboussi, Jamshid; Wu, Xinzhou; Kaklauskas, Gintaris

doi:10.1080/13921525.1999.10531472

Cited by 8 publications

(5 citation statements)

References 12 publications

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“…• FFNN is used in [44,45] to model the material behavior at the macroscale level, using strains (as inputs) and stresses (as outputs). One main advantage of such a model is that the training data required for the neural network can be directly acquired from experimental data.…”

Section: Deep Learning (Dl) Architecturesmentioning

confidence: 99%

Feed-Forward Neural Networks for Failure Mechanics Problems

2021

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This work addresses an efficient neural network (NN) representation for the phase-field modeling of isotropic brittle fracture. In recent years, data-driven approaches, such as neural networks, have become an active research field in mechanics. In this contribution, deep neural networks—in particular, the feed-forward neural network (FFNN)—are utilized directly for the development of the failure model. The verification and generalization of the trained models for elasticity as well as fracture behavior are investigated by several representative numerical examples under different loading conditions. As an outcome, promising results close to the exact solutions are produced.

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Section: Deep Learning (Dl) Architecturesmentioning

confidence: 99%

Feed-Forward Neural Networks for Failure Mechanics Problems

2021

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“…The output variable Y of DNN is given by

where

represents the activation function,

denotes the weight,

refers to the j the input signal and

represents the bias. Sigmoid activation function is usually employed as the activation function in the DNN algorithm [ 32 , 33 , 34 ], which is expressed as follows:

where x is given by

and

represents the sigmoid function steepness parameter.…”

Section: Deep Neural Networkmentioning

confidence: 99%

Modeling of Mechanical Properties of Clay-Reinforced Polymer Nanocomposites Using Deep Neural Network

2020

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Due to the non-linear characteristics of the processing parameters, predicting the desired properties of nanocomposites using the conventional regression approach is often unsatisfactory. Thus, it is essential to use a machine learning approach to determine the optimum processing parameters. In this study, a backpropagation deep neural network (DNN) with nanoclay and compatibilizer content, and processing parameters as input, was developed to predict the mechanical properties, including tensile modulus and tensile strength, of clay-reinforced polyethylene nanocomposites. The high accuracy of the developed model proves that DNN can be used as an efficient tool for predicting mechanical properties of the nanocomposites in terms of four independent parameters.

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“…In Reference 23, the representation of the constitutive relation through a neural network was among the pioneering contributions. At that time, the learning of strain‐stress mapping was purely data‐driven, which means that no physical knowledge was neither enforced in the network architecture nor informed in the loss function.…”

Section: Introductionmentioning

confidence: 99%

NN‐mCRE: A modified constitutive relation error framework for unsupervised learning of nonlinear state laws with physics‐augmented neural networks

Benady,

Baranger,

Chamoin

2024

Numerical Meth Engineering

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This article proposes a new approach to train physics‐augmented neural networks with observable data to represent mechanical constitutive laws. To train the neural network and learn thermodynamics potentials, the proposed method does not rely on strain‐stress or strain‐free energy pairs but needs only partial strain or displacement measurements inside the structure. The neural network is trained thanks to an unsupervised procedure in which the modified constitutive relation error (mCRE) is minimized. The mCRE functional provides a bias‐aware data assimilation framework with a rich physical sense as the constitutive relation error (CRE) part can be interpreted as a modeling error continuously defined over the structure, and can be used as a prediction quality in the inference phase. This article also extends previous works on the mCRE by introducing a new minimization procedure in the case of nonlinear state laws. As typical structural health monitoring applications may require that the neural networks should be trained online, an important focus is thus made on automatic and adaptive tuning of sensitive hyperparameters (learning rate, weighting between losses, number of epochs and initialization). It is shown that when the training database is rich enough with respect to the loading cases, the proposed method achieves remarkable performance regarding the quality of the learned model, noise robustness, and low sensitivity to user‐defined hyperparameters. The method is evaluated on two test cases: a non‐quadratic potential in the small strain regime with synthetic optic fiber measurements, and a Mooney–Rivlin model in the hyperelastic case with synthetic digital image correlation observations.

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Neural Network Material Modelling

Cited by 8 publications

References 12 publications

Feed-Forward Neural Networks for Failure Mechanics Problems

Feed-Forward Neural Networks for Failure Mechanics Problems

Modeling of Mechanical Properties of Clay-Reinforced Polymer Nanocomposites Using Deep Neural Network

NN‐mCRE: A modified constitutive relation error framework for unsupervised learning of nonlinear state laws with physics‐augmented neural networks

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